When u hold a paper and try to apply tensile force it is going to fail at the point of gripping why it is so?

Question

Try it, it is going to fail near gripping. Let us consider a similar situation "A tensile specimen" tested in lab it is going to fail with in the gauge length.

Answer 1

The two results are perfectly consistent. Material fails at the location of the highest stress.

In a tensile specimen, the gauge length typically has smaller cross section than the ends where the sample is gripped. That means that for a given uniaxial load, the stresses are much higher in the gauge length than at the gripped ends. The material is going to fail at the higher stress location first, which is why it fails in the gauge length section rather than the grip. It is possible to make the sample fail at the grip, but that's typically because the grip is poor, misaligned, or is severely causing damage to the specimen by the very process of gripping.

When use a plain sheet of rectangular paper, it fails at the gripping point because you have a local stress concentration there. That's where the highest stress is. If you cut that paper into the shape of a tensile specimen and do it again, it won't fail at the grip. It'll fail at the thinned section because that's where the highest stress now is.

Answer 2

It fails near the gripping point because that's where the force per cross-section area (stress) is greatest. Out near the middle of the paper, the same force is distributed over a greater cross-section area. Your observation about samples tested in a lab is correct. That's why such samples are always narrowest at their midlength, with plenty of extra material where it will be attached to the testing apparatus. You can do the same by trimming your paper sample to form a narrow "waist" where you wish it to break. Use the dimensions of the waist when calculating the paper's tensile strength.

Answer 3

There is a stress consentration at the gripping point. If you can grip the specimen perfectly so the stress is consistent all the wat across then it will fail at a localized flaw in the subject. Seldom in the guage length